Question

Ernesto solves the equation below by first squaring both sides of the equation. \sqrt{\dfrac{1}{2}w+8}=-2 2 1 ​ w+8 ​ =−2square root of, start fraction, 1, divided by, 2, end fraction, w, plus, 8, end square root, equals, minus, 2 What extraneous solution does Ernesto obtain?

Answer 1

w = -8

Explanation:

Given the equation solved by Ernesto expressed as
`\sqrt{(1)/(2)w+8}=-2`, the extraneous solution obtained by Ernesto is shown below;

`\sqrt{(1)/(2)w+8}=-2\\\\square\ both \ sides \ of \ the \ equation\\(\sqrt{(1)/(2)w+8})^2=(-2)^2\\\\(1)/(2)w+8 = 4\\\\Subtract \ 8 \ from \ both \ sides\\\\(1)/(2)w+8 - 8= 4- 8\\\\(1)/(2)w= -4\\\\multiply \ both \ sides \ by \ 2\\\\(1)/(2)w*2= -4*2\\\\w = -8`

Hence, the extraneous solution that Ernesto obtained is w = -8